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Electrochemical double-layer capacitors with micro-to-nanoporous electrodes based on activated carbon utilize the gross interface between carbon and the electrolyte, which fills the pores of two main classes, ͑i͒ micrometer voids between agglomerates of carbon grains and (ii) micro-to-nanometer pores inside agglomerates and grains. The bigger pores provide good transport of ions throughout the layer whereas the smaller pores generate a large interfacial area. This essentially bifunctional architecture prompted us to combine two complementary concepts in the pertinent theory of double-layer capacitors, viz. linear transmission line models and self-affine fractal models. The merit of this structure-based approach, involving also the effect of hindrance of ionic conductivity in nanopores, is that it relates basic structural characteristics to the dynamic performance. Practically, with no fitting parameters, it reproduces the main features of recently reported complex impedance data. This refers to the effect of electrode thickness, constant phase angle ͑CPA͒ and crossover between CPA and non-CPA behavior. Routes toward the optimization of the capacitor architecture for the largest possible static capacitances and rapid charging-discharging are explored. The comparison of calculated optimum capacitance values with recent experimental data reveals remarkable reserves for advanced structural design.

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Supercapacitor (SC) cells based on microporous titanium carbide-derived carbon [C(TiC)] electrodes in room temperature ionic liquid (1-ethyl-3-methylimidazolium tetrafluoroborate) have been tested by cyclic voltammetry, constant current charge/discharge, and electrochemical impedance methods at temperatures from 25 to 80°C . The limits of ideal polarizability, low frequency limiting capacitance and series resistance, time constant, complex power components, time stability, and other characteristics have been calculated and discussed. The influence of temperature on the cell capacitance, characteristic time constant values, and region of ideal polarizability has been analyzed. The comparatively high energy (40Whkg−1) and power (130kWkg−1) densities per active C(TiC) weight have been calculated, weakly depending on temperature, if T≤59°C . A comparison of the results to the corresponding data for the C(TiC)∣1M(normalC2normalH5)3CH3NBF4+acetonitrile system indicates that 1-ethyl-3-methylimidazolium tetrafluoroborate∣carbide -derived carbon SC cells demonstrate lower power densities, a narrower region of ideal polarizability, and a lower constant current cyclability at higher charge/discharge rates.

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